Question

ex 11 va rog din suflet dau coroana si 50 puncte

Answer 1

 tinem cont ca 7+7²+7³=7+49+343
atunci

a=1*(7+49+343) +7³(7+49+343)+7^6(7+49+343)+...+7^297(7+49+343)=
399(1+7³+7^6+...+7^297)=21*19(1+7³+7^6+...+7^297),divizibil cu 19
grea!!

Answer 2

11)
a = 7+7^2+7^3+7^4+7^5+7^6+...+7^298+7^299+7^300

grupam cate trei,termenii sumei si dam factor comun:

a = 7×(1+7+7^2)+7^4×(1+7+7^2)+...+7^298×(1+7+7^2)

a = 7 × 57 + 7^4 × 57 +...+ 7^298 × 57

a = 57 × (7 + 7^4 +...+ 7^298) divizibil cu 19 (57 : 19 = 3)